BANBEIS
Developing Mathematical Algorithms and Softwares for the Model Reduction of Large-Scale Dynamical Systems. (MS20191055)
- Funded by: Bangladesh Ministry of Education (BANBEIS)
- Principle Investigator: Dr. Mohammad Monir Uddin (monir.uddin@northsouth.edu)
- Co-Principle Investigator: Prof Dr. Farahad Uddin (BUET) (forhad@math.buet.ac.bd)
- Duaration: 3 years (Started from November 2019)
Project Laboratory
Team
Project Outcome
Model order reduction (MOR) is considered as an indispensable subject in the different branches of Science, Engineering and Technology. The demand of MOR is increasing everyday in the different branches of Science, Engineering and Technology. The main goal of this research is to develop robust algorithms and software using different prominent methods of the MOR. The possible significant outcomes of this research are as follows:
- The algorithms and software developed from this research would be interesting and rewarding materials for further research and development in both academics and industries.
- The software can be useful in Industries for the controller design, optimization and simulation of large-scale mathematical models.
- With the results of this project besides several journal papers we also can publish a book.
- The researches will be benefited tremendously. The project will help them to acquire knowledge in Control theory, Optimizations, Scientific computing, Mathematical Algorithms and Software. They can see how to apply the Mathematical knowledge in the real life applications. Moreover, if necessary the obtained results may help them to obtain PhD or MPhil Degrees.
We have planned to complete the project as the following steps:
- 1st year: Literature Review, understanding the problems and developing some fundamental algorithms and software.
- 2nd year: Developing algorithms and software for the model reduction of model reduction of large-scale descriptor systems, some numerical experiments and pressing in conferences.
- 3rd year: Numerical experiments with the rigorous data in a high performance computer lab and preparing and submitting papers and book for publications.
Sumulation & Results
Publications
Computational techniques for H2 optimal frequency-limited model order reduction of large-scale sparse linear systems
Journal of Computational Science
We consider the problem of frequency limited H2 optimal model order reduction for large-scale sparse linear systems. A set of first-order H2 optimality conditions are derived for the frequency limited model order reduction problem.JOURNAL
Computational techniques for H2 optimal frequency-limited model order reduction of large-scale sparse linear systems
About The Publication
We consider the problem of frequency limited H2 optimal model order reduction for large-scale sparse linear systems. A set of first-order H2 optimality conditions are derived for the frequency limited model order reduction problem. These conditions involve the solution of two frequency limited Sylvester equations that are known to be computationally complex. We discuss a framework for solving these matrix equations efficiently. The idea is also extended to the frequency limited H2 optimal model order reduction of index-1 descriptor systems. Numerical experiments are carried out using Python programming language and the results are presented to demonstrate the approximation accuracy and computational efficiency of the proposed technique.
Tangential interpolatory projections for a class of second-order index-1 descriptor systems and application to Mechatronics
Production Engineering
This paper studies the model order reduction of second-order index-1 descriptor systems using a tangential interpolation projection method based on the Iterative Rational Krylov Algorithm (IRKA).JOURNAL
Tangential interpolatory projections for a class of second-order index-1 descriptor systems and application to Mechatronics
About The Publication
This paper studies the model order reduction of second-order index-1 descriptor systems using a tangential interpolation projection method based on the Iterative Rational Krylov Algorithm (IRKA). Our primary focus is to reduce the system into a second-order form so that the structure of the original system can be preserved. For this purpose, the IRKA based tangential interpolatory method is modified to deal with the second-order structure of the underlying descriptor system efficiently in an implicit way. The paper also shows that by exploiting the symmetric properties of the system the implementing computational costs can be reduced significantly. Theoretical results are verified for the model reduction of the piezo actuator based adaptive spindle support which is second-order index-1 differential-algebraic form. The efficiency and accuracy of the method are demonstrated by analyzing the numerical results.
Stability Preservation of Frequency-Limited Balancing Based Reduced Order Model of Large Scale Index-1 Descriptor System
11th International Conference on Electrical and Computer Engineering (ICECE)
This paper discusses on the stability preservation technique of the frequency limited balanced reduced order model of a class of large-scale sparse descriptor system.CONFERENCES
Stability Preservation of Frequency-Limited Balancing Based Reduced Order Model of Large Scale Index-1 Descriptor System
About The Publication
This paper discusses on the stability preservation technique of the frequency limited balanced reduced order model of a class of large-scale sparse descriptor system. For this purpose, firstly we modify standard rational Krylov subsapce method (RKSM) for solving frequency-limited Lyapunov equation pair to find out low-rank Gramian factors what is necessary to apply in balanced truncation technique. Next, we construct two projector matrices, and project the balanced unstable reduced system matrices found after implementing balanced truncation technique to ensure stability. Several data of index-1 descriptor system models are nominated for numerical experiments to demonstrate the efficiency of the proposed technique.
In search of frequency-limited low-rank Gramian factors for the balancing based model reduction of large-scale sparse descriptor system
23rd International Conference on Computer and Information Technology (ICCIT)
his paper discusses frequency limited balanced truncation of a class of large-scale sparse descriptor system by preserving the sparsity of the system.CONFERENCES
In search of frequency-limited low-rank Gramian factors for the balancing based model reduction of large-scale sparse descriptor system
About The Publication
This paper discusses frequency limited balanced truncation of a class of large-scale sparse descriptor system by preserving the sparsity of the system. For this purpose we compute the low-rank Gramian factors by solving the frequency limited Lyapunov equations. We modify the standard rational Krylov subspace method (RKSM) for solving the Lyapunov equations efficiently and implicitly. Several data of index-l descriptor system models are nominated for numerical experiments to demonstrate the efficiency of the proposed techniques.
ERROR MINIMIZATION OF REDUCED MODELS OF LARGE-SCALE SYSTEMS BY SOLVING TIME AND FREQUENCY RESTRICTED LYAPUNOV EQUATIONS
Master’s thesis, Buet
The usage of mathematical models of physical systems are increasing day by day in various disciplines of science and engineering for simulation, optimization, or control. Descriptor systems is a special kind of formation of physical systems arisen in many practical oriented fields whose dynamics maintain Differential- Algebraic Equations.THESES
ERROR MINIMIZATION OF REDUCED MODELS OF LARGE-SCALE SYSTEMS BY SOLVING TIME AND FREQUENCY RESTRICTED LYAPUNOV EQUATIONS
About The Publication
The usage of mathematical models of physical systems are increasing day by day in various disciplines of science and engineering for simulation, optimization, or control. Descriptor systems is a special kind of formation of physical systems arisen in many practical oriented fields whose dynamics maintain Differential- Algebraic Equations. Such type of systems are originated by finite elements or difference methods which becomes huge and complex to analyze along with the increment of the fineness of the grid resolution. As a result, the necessity of model order reduction comes up in order to minimize the complexity of the models during controlling by preserving the input-output relation of the original large-scale models. However, although reducing the dimension of large-scale models on infinite time and frequency domains has a great theoretical significance, the reduced order models of original large-scale models on restricted time and frequency intervals are more demandable to the analyzers and engineers for practical investigation. This dissertation elaborately discusses the model generations for data extraction to form the large-scale state-space systems and the projection based techniques to calculate the approximate low-rank solutions of the original state-space systems on definite time and frequency intervals. We impose relevant governing equations to create physical as well as data models. Balanced truncation is one of the most notable methods for the reduction of the model dimensions of linear time-invariant systems which requires computing the numerical solutions of two Lyapunov equations, commonly known as Gramians. Among some widely used approaches, Rational Krylov Subspace Method is one of the most effective procedures for finding the Gramians of the Lyapunov equations of the large-scale sparse dynamical systems which has already been developed to compute the low-rank time and frequency indefinite solutions. Besides, it has been also reformed to compute the low-rank approximation of the standard Lyapunov equations on limited time and frequency intervals for small-dense state-space systems.
Computational techniques for riccati-based feedback stabilization of large-scale sparse index-2 descriptor system
Master’s thesis, Buet
This thesis mainly focuses on computational techniques applied to stabilize unstable Navier-Stokes models. The models arising from the Navier stokes equation are an essential aspect in engineering applications and applied mathematics in fluid mechanics, which is significantly depends on Reynolds number (Re), and if Re?300, the corresponding model will be unstable.THESES
Computational techniques for riccati-based feedback stabilization of large-scale sparse index-2 descriptor system
About The Publication
This thesis mainly focuses on computational techniques applied to stabilize unstable Navier-Stokes models. The models arising from the Navier stokes equation are an essential aspect in engineering applications and applied mathematics in fluid mechanics, which is significantly depends on Reynolds number (Re), and if Re?300, the corresponding model will be unstable. The computation steps are designed to approximate the full models with the ROMs, find the reduced-order feedback matrices, and attain the optimal feedback matrices for stabilizing the desired Navier-Stokes models. The prime concern is exploring the Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flow via Krylov subspace techniques. Since the volume of data derived from the original models is large, the feedback stabilization process through the Riccati equation is always infeasible. Therefore, a H_2 optimal model-order reduction scheme for reduced-order modeling, preserving the sparsity of the system, is required. Some conventional methods exist, but they have some adversities, such as the requirement of high computation time and memory allocation, complex matrix algebra, and uncertainty of the stability of the reduced-order models. To overcome these drawbacks, an extended form of Krylov subspace-based Two-Sided Iterative Algorithm (TSIA) is implemented to stabilize non-symmetric index-2 descriptor systems explored from unstable Navier-Stokes models. The proposed techniques are sparsity-preserving and utilize the Wilson condition to efficiently satisfy the reduced-order modeling approach through the sparse-dense Sylvester equations. To solve the desired Sylvester equations, sparsity-preserving Krylov subspaces are structured via the system of linear equations with a compact form of matrix-vector operations. Inverse projections approaches are applied to get the optimal feedback matrix from reduced-order models. To validate the efficiency of the proposed techniques, transient behaviors of the target systems are observed, incorporating the tabular and figurative comparisons with MATLAB simulations. Finally, to reveal the advancement of the proposed techniques, we compare our work with some existing results. From the tabular and graphical comparisons of the results of numerical computations, it is observed that RKSM is not applicable for the target models due to the non-symmetric structure. In contrast, TSIA can be suitably applied to solve Sparse-dense Sylvester equations for reduced-order modeling. Furthermore, by the TSIA, full models can be efficiently approximated by the corresponding ROMs with minimized H_2 error norm, and the inverse projection scheme is effective in computing the optimal feedback matrices from the reduced-order feedback matrices to stabilize the target models more efficiently than existing methods. Thus, it can be concluded that by utilizing TSIA, unstable Navier-Stokes models can be stabilized with better accuracy and less computing time.
Pothole Detection System Using Region-Based Convolutional Neural Network
2021 IEEE 4th International Conference on Computer and Communication Engineering Technology (CCET)
Street surface weakening, for example, potholes, has caused drivers substantial money-related harm each year. Notwithstanding, viable street condition observing has been a proceeding with a challenge to street proprietors.CONFERENCES
Pothole Detection System Using Region-Based Convolutional Neural Network
About The Publication
Street surface weakening, for example, potholes, has caused drivers substantial money-related harm each year. Notwithstanding, viable street condition observing has been a proceeding with a challenge to street proprietors. Profundity cameras have a small field of view and can be effectively influenced by vehicle bobbing. Customary picture handling strategies are dependent on calculations. For example, the division can't adjust to shifting ecological and camera situations. In this paper, the object detection API for pothole detection is used to test the set of images and videos and give the output results of the tested images and videos. By evaluating the R-CNN algorithm and SSD mobile net algorithm, the results of the test showed successful results in getting potholes from test images with a maximum confidence level of 93%.